If $f(x) = -3x + 3$, Find $f(-2$\].$f(-2) =$

In mathematics, a function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range. It is a way of describing a relationship between variables. In this article, we will explore the concept of function evaluation, specifically for the given function $f(x) = -3x + 3$. We will learn how to evaluate the function at a specific value of $x$, and apply this concept to find the value of $f(-2)$.

What is a Function?

A function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range. It is a way of describing a relationship between variables. In other words, a function takes an input, called the argument, and produces an output, called the value of the function.

The Given Function

The given function is $f(x) = -3x + 3$. This function takes an input $x$ and produces an output $f(x)$, which is calculated using the formula $-3x + 3$.

Evaluating the Function at a Specific Value

To evaluate the function at a specific value of $x$, we simply substitute the value of $x$ into the formula for the function. For example, to evaluate the function at $x = -2$, we substitute $-2$ into the formula:

$f(-2) = -3(-2) + 3$

Simplifying the Expression

To simplify the expression, we first evaluate the product $-3(-2)$:

$-3(-2) = 6$

Then, we add $3$ to the result:

$f(-2) = 6 + 3$

Finding the Value of $f(-2)$

Finally, we add $6$ and $3$ to find the value of $f(-2)$:

$f(-2) = 9$

Therefore, the value of $f(-2)$ is $9$.

Conclusion

In this article, we learned how to evaluate the function $f(x) = -3x + 3$ at a specific value of $x$. We applied this concept to find the value of $f(-2)$, which is $9$. This demonstrates the importance of function evaluation in mathematics, and how it can be used to solve problems and make predictions.

Real-World Applications

Function evaluation has many real-world applications, including:

• Physics and Engineering: Function evaluation is used to model real-world phenomena, such as the motion of objects and the behavior of electrical circuits.
• Economics: Function evaluation is used to model economic systems, such as supply and demand curves.
• Computer Science: Function evaluation is used to develop algorithms and solve problems in computer science.

Common Mistakes to Avoid

When evaluating a function at a specific value of $x$, it is easy to make mistakes. Here are some common mistakes to avoid:

• Not substituting the value of $x$ into the formula: Make sure to substitute the value of $x$ into the formula for the function.
• Not simplifying the expression: Make sure to simplify the expression after substituting the value of $x$ into the formula.
• Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when simplifying the expression.

Final Thoughts

$$$$

In this article, we will answer some common questions related to function evaluation. Whether you are a student, a teacher, or simply someone who wants to learn more about function evaluation, this article is for you.

Q: What is function evaluation?

A: Function evaluation is the process of finding the value of a function at a specific value of the input variable. In other words, it is the process of substituting a value of the input variable into the formula for the function and simplifying the expression to find the output value.

Q: Why is function evaluation important?

A: Function evaluation is important because it allows us to solve problems and make predictions in a variety of fields, including physics, engineering, economics, and computer science. By understanding how to evaluate a function at a specific value of the input variable, we can model real-world phenomena and make informed decisions.

Q: How do I evaluate a function at a specific value of the input variable?

A: To evaluate a function at a specific value of the input variable, you simply substitute the value of the input variable into the formula for the function and simplify the expression. For example, if we want to evaluate the function f(x) = -3x + 3 at x = -2, we would substitute -2 into the formula and simplify the expression:

f(-2) = -3(-2) + 3 f(-2) = 6 + 3 f(-2) = 9

Q: What are some common mistakes to avoid when evaluating a function?

A: Some common mistakes to avoid when evaluating a function include:

• Not substituting the value of the input variable into the formula
• Not simplifying the expression
• Not following the order of operations (PEMDAS)

Q: How do I know if I have evaluated a function correctly?

A: To check if you have evaluated a function correctly, you can plug the value of the function back into the original equation and see if it is true. For example, if we want to check if f(-2) = 9 is true, we can plug 9 back into the original equation:

f(-2) = -3(-2) + 3 f(-2) = 6 + 3 f(-2) = 9

Since 9 is equal to 9, we know that f(-2) = 9 is true.

Q: Can I use function evaluation to solve problems in other fields?

A: Yes, function evaluation can be used to solve problems in other fields, including physics, engineering, economics, and computer science. By understanding how to evaluate a function at a specific value of the input variable, you can model real-world phenomena and make informed decisions.

Q: What are some real-world applications of function evaluation?

A: Some real-world applications of function evaluation include:

• Modeling the motion of objects in physics
• Modeling the behavior of electrical circuits in engineering
• Modeling the behavior of economic systems in economics
• Developing algorithms in computer science

Q: How can I practice function evaluation?

A: You can practice function evaluation by working through examples and exercises in a textbook or online resource. You can also try evaluating functions at different values of the input variable to see how the output value changes.

Q: What are some common functions that I should know how to evaluate?

A: Some common functions that you should know how to evaluate include:

• Linear functions (e.g. f(x) = -3x + 3)
• Quadratic functions (e.g. f(x) = x^2 + 2x + 1)
• Polynomial functions (e.g. f(x) = x^3 - 2x^2 + x - 1)
• Rational functions (e.g. f(x) = x^2 / (x + 1))

By understanding how to evaluate these functions, you will be able to solve problems and make predictions in a variety of fields.